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Nearest Neighbour Decision Rule for Non-Parametric Classification

Understand the effectiveness of the Nearest Neighbour decision rule in non-parametric classification. Learn how this rule can be used in situations where other classification methods may not work. Explore its asymptotic performance compared to the Bayes rule.

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Nearest Neighbour Decision Rule for Non-Parametric Classification

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  1. Non-Parametric: K-NN Prof. A.L. Yuille Stat 231. Fall 2004. Duda, Hart and Stork: Chp 4.4 & 4.5.

  2. K-NN.

  3. K-NN

  4. K-NN Examples.

  5. Non-parametric Classification.

  6. Non-Parametric Classification

  7. Nearest Neighbour Decision Rule

  8. Nearest Neighbour Decision Rule

  9. Nearest Neighbour Decision Rule

  10. Randomized Decisions.

  11. NN Error Analysis Here x* is the sample closest to point x. As the no. samples becomes large x* will be arbitrarily close to x.

  12. NN Error Analysis

  13. NN Error Analysis

  14. NN Error Analysis

  15. KNN Decision Rule

  16. NN Decision Rule • The nearest neighbour decision rule is very easy to use. • It can be effective in situations where other classification rules – e.g. linear separation – will not work. • The asymptotic result shows that the NN rule often approaches the performance of the (optimal) Bayes rule.

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